Fritz von Haeseler

Pascal's triangle, dynamical systems and attractors

This paper establishes a global dynamical systems approach for the fractal patterns which are obtained when analysing the divisibility of binomial coefficients modulo a prime power. The general framework is within the class of hierarchical iterated function systems. As a consequence we obtain a complete deciphering of the hierarchical self-similarity features.

Global analysis of self-similarity features of cellular automata: selected examples

Abstract The analysis of self-similarity properties of the evolution patterns of linear cellular automata is investigated using the theory of hierarchical iterated function systems and substitution systems. We present several selected examples.

Linear Cellular Automata, Substitutions, Hierarchical Iterated Function Systems and Attractors

Many constructions and algorithms from fractal geometry have become fundamental tools within the naturalism program of computer graphics. As the interest of computer graphics is shifting towards new frontiers such as scientific visualization some other basic concepts from fractal geometry come into focus. Cellular automata (CA) in particular are becoming a premier modelling and simulation tool in engineering and the basic sciences. CA live in a discrete world and are local in nature. They produce structure and patterns subject to a set of rules (look-up table) which determine the state of a growing cell from the state of its neighbors.

SELF-SIMILAR STRUCTURE OF RESCALED EVOLUTION SETS OF CELLULAR AUTOMATA I

The self-similarity properties of the orbits of a class of cellular automata are deciphered by matrix substitutions, hierarchical iterated function systems and appropriate scaling procedure.

Coarse-graining invariant patterns of one-dimensional two-state linear cellular automata

We consider one-dimensional two state cellular automata and their orbital patterns. We are particulary interested in initial states and their orbital pattern which are invariant under a certain coarse-graining operation. We show that invariant initial states are automatic. Moreover, we numerically study the complex nature of the initial states and their invariant orbits.

Surgery for relaxed newton's method

In this paper we consider Newtons method with the help of quasi conformal surgery. Using holomorphic motions the existence of attractive periodic points of relaxed Newtons method for cubic polynomials and any h ∊]0,1[ is established.

RESCALED EVOLUTION SETS OF LINEAR CELLULAR AUTOMATA ON A CYLINDER

Rescaled evolution sets of linear cellular automata on a lattice ℤ ⊕ G, where G is a finite Abelian group, with states in the finite field

Linear cellular automata and automatic sequences

{\mathbb F}_q

Automaticity of Solutions of Mahler Equations

are defined and investigated.

Symmetric self-organization in a cellular automaton requiring an essentially random feedback. Observations, conjectures, questions

We study one-dimensional linear cellular automata with values in a finite ring. The orbit of an initial configuration can be considered as a double sequence. We study the generated double sequence from the point of view of automatic sequences. We present several results which show the usefulness of this concept in the study of cellular automata. Furthermore, we present some results which are related to similar questions.